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The ends of the major axis of an ellipse are (- 2, 4) and (2, 1). If the point (1, 3) lies on the ellipse,then find its latus rectum and eccentricity. |
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Answer» the major end points are (-2,4),(2,1) by distance formula `2a=sqrt(4^2+3^2)` `2a=sqrt(16+9)` `2a=5` `a=5/2` center of eclipse `((-2+2)/2,(4+1)/2)` equation of eclipse `(x-0)^2/a^2+(y-(5/2))^2/b^2=1` `x^2/(25/4)+(y-(5/2))^2/b^2=1` now, we have to find b putting the value(1,3) `4/25+1/4b_2=1` `1/4b^2=1-4/5=21/25` so `b^2=25/84` `x^2/(25/4)+(y-(5/2))^2/b62=1` length of latus rectum will be`=2b^2/a=(2*25*2)/(84*5)=5/21` eccentricity=`e=sqrt(1-b^2/a^2)=sqrt(1-(25/84)/(25/4)=sqrt(20/21)`. |
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